It is consistent that there is a set mapping from the four-tuples of n into the finite subsets with no free subsets of size tn for some natural number tn. For any n < it is con...
We consider a finite universe U (more exactly - a family U of them), second order quantifiers QK , where for each U this means quantifying over a family of n(K)-place relations clo...
f orderings provide an abstract framework in which to study spaces of orderings of formally real fields. Spaces of orderings of finite chain length are well understood [9] [12]. Th...
In this paper we show that the compactness of a Loeb space depends on its cardinality, the nonstandard universe it belongs to and the underlying model of set theory we live in. In...
We extend the notion of limitwise monotonic functions to include arbitrary computable domains. We then study which sets and degrees are support increasing (support strictly increas...